2005 - Talksequation together with the Kahler-Ricci flow on complete non-compact manifolds, we...

2005 - Talks Contact Marie Taris for details.

MATHEMATICS TALKS LIST

2005

JANUARY

Colloquium Thursday,1/20/2005 Talk: 4:30, Tea: 4:00 Room: 199 Host: Prof. Guido Weiss

Speaker: Prof. Akram Aldroubi Vanderbilt University

Title: Convolution, Average Sampling and Calderon Resolution of the Identity for Shift-Invariant Spaces

Wavelet Seminar Friday, 1/21/2005 Time: 3:30pm Room: 199 Host: Prof. Guido Weiss

Speaker: Prof. Akram Aldroubi Vanderbilt University

Title: Wavelets on an irregular grid

Analysis Seminar Wednesday, 1/26/2005 Time: 4-5 Room: 199 Host: Prof. John McCarthy

Speaker: Organizational Meeting Only, No Speaker

Title:

Colloquium Thursday, 1/27/2005 Talk: 4:30, Tea: 4:00 Room: 199 Host: Prof. N. Mohan Kumar

Speaker: Prof. David Fisher City University of New York

Title: Local Rigidity and First Cohomology

Abstract: In 1964, Andre Weil showed that a homomorphism _ from a finitely generated group _ to a Lie group G is locally rigid whenever H1(_, g) = 0. Here _ is

locally rigid if any nearby homomorphism is conjugate to _ by a small element of G, and g is the Lie algebra of G. The point of my talk is describe an infinite dimensional

�analog of Weil s theorem: Theorem 0.1. Let _ be a finitely presented group, (M, g) a compact Riemannian manifold and _ :_!Isom(M, g)_Diff1(M) a homomorphism. Then if H1(_,Vect1(M)) = 0, the homomorphism _ is locally rigid as a homomorphism into Diff1(M). This work is motivated by a string of results by many authors, beginning with Zimmer, generalizing results about finite dimensional representations of lattices in Lie groups to representations taking values in diffeomorphism groups. I will give history and motivation for the subject, including a discussion �of Weil s original motivation. I will also describe a simple criteria for vanishing of H1(_,Vect1(M)), and give applications for three classes of groups. Some of these applications are quite surprising and others give new and simpler proofs of old results. If time permits, I will also discuss some related examples for which either rigidity does not hold or for which

�H1 doesn t vanish but rigidity might still hold.

Wavelet Seminar Friday, 1/28/2005 Time 3:30 Room: 199 Host: Prof. Guido Weiss

Speaker: Wang-Q Lim Washington University Graduate Student

Title: Method(s) for obtaining "smooth" and "localized" composite wavelets

Seminar Friday, 1/28/2005 Time 4-5:30 Room: 111 Host: Prof. N. Mohan Kumar

Speaker: Prof. A. Prabhakar Rao University of Missouri, St. Louis

Title: Chern class formalism for vector bundles on schemes

Colloquium Monday, 1/31/2005 Talk: 4:30, Tea: 4:00 Room: 199 Host: Prof. N. Mohan Kumar

Speaker: Prof. Ilan Hirshberg University of Southern Denmark, Denmark

Title: Endomorphism semigroups, product systems and Arveson's spectral C*-algebras

FEBRUARY

Colloquium Wednesday, 2/2/2005 Talk: 4:30, Tea: 4:00 Room: 199 Host: Prof. N. Mohan Kumar

Speaker: Prof. Tao Li Oklahoma State University

Title: Heegaard surfaces, measured laminations and the Waldhausen conjecture

Abstract: A Heegaard splitting is a decomposition of a 3-manifold into a pair of handlebodies along an embedded surface, called Heegaard surface. Every closed 3-manifold has a Heegaard splitting. The Waldhausen conjecture says that a 3-manifold

has only a finite number of inequivalent minimal (or irreducible) Heegaard splittings. We will study the limit of a sequence of compact surfaces in the measured lamination space, and give a complete solution to the Waldhausen conjecture. We will also discuss some applications and open problems.

Colloquium Thursday, 2/3/2005 Talk: 4:30, Tea: 4:00 Room: 199 Host: Prof. Zhengjun Zhang

Speaker: Prof. Rong Chen Department of Information and Decision Sciences University of Illinois, Chicago, Department of Business Statistics and Economics, Peking University

Title: Threshold Variable Selection and Threshold Variable Driven Switching Autoagressive Models

Abstract: As one of the most important classes of nonlinear time series models, Threshold Autoregressive (TAR) models have been successfully applied in many fields. The process switches between two (or more) different linear models. The switching dynamics is predictable (in short term), since it is assumed to be deterministically driven by an observable threshold variable. Hence, choosing an appropriate threshold variable is an important, but difficult task. The random (Markovian) Switching Autoregressive (SAR) model is a special case of the threshold family. It avoids the difficulty of selecting the threshold variable, and allows certain flexibility in the switching mechanism. But it provides less information on the true nature of the switching mechanism, therefore causes difficulty in prediction. In this talk we propose a new class of nonlinear time series models, which combines the threshold model and the random switching model. This model relies on an observable threshold variable as used in a TAR model, hence reveals the true nature of the switching mechanism. It also allows certain randomness in the switching procedure similar to that in a SAR model, which provides some flexibility. Furthermore, we propose a model building procedure that concentrates on a fast determination of an appropriate threshold variable among a large set of candidates (and linear combination of them). It starts with classification (clustering) of observations into two (or more) classes. This preliminary classification forms the basis for fast searching. Once a small number of threshold variable candidates are identified, the full models are estimated, and model selection is carried out via certain criteria. A simulation study and two real data examples are presented.

Wavelet Seminar Friday, 2/4/2005 Time 3:30 Room: 199 Host: Prof. Guido Weiss

Speaker: Demetrio Labate North Carolina State University

Title: Work by M. Do and M. Vetterli on the contourlet tranasform

Seminar Friday, 2/4/2005 Time 4-5:30 Room: 111 Host: Prof. N. Mohan Kumar




Speaker: Prof. Michael Goldberg California Institute of Technology

Title: Dispersive Bounds for the Schr\"odinger Equation with Almost Critical Potentials

Abstract: Solutions to the Schr\"odinger equation are constrained in their evolution by several families of inequalitites, among them the dispersive bounds. These typically control the $L^{p'}$ norm of a solution at time $t$ in terms of the $L^p$ norm of the initial data and a polynomially decaying factor of the time elapsed. The familiar law of conservation of mass is expressed here in the special case $p = 2$. In this talk I will address the question: Are the dispersive bounds still valid in the presence of a time-independent potential, and if so, under what conditions? In the three-dimensional setting, the following criteria are known to be sufficient: An integrability condition regulating the singularities and decay of the potential, and a zero-energy condition on the associated Hamiltonian. It is not necessary to assume that the potential posesses and additional regularity, positivity, or smallness. I will sketch a proof of this theorem, and describe the best known results in other dimensions.

Graduate Seminar Tuesday, 2/8/2005 Time 4:30-5:30, Pizza: 5:30-6 Room: 199 Host: Prof. Gary Jensen

Speaker: Prof. Ed Wilson Washington University

Title: Shift invariant spaces

Abstract: A shift invariant space is a closed subspace of a Hilbert space on which some countable group of unitary operators acts and for which the action of the group on a certain set of generators produces an orthonomormal basis of the subspace. There are lots of variations on this theme, especially when the group isn't commutative. The theory of shift invariant spaces is reminiscent of things studied in 431 despite the fact that the interesting spaces, groups, and rings are all infinite. Shift invariant spaces are used heavily in the study of wavelets and other reproducing function systems.

Analysis Seminar Wednesday, 2/9/2005 Time 4:00 Room: 199 Host: John McCarthy

Speaker: Prof. Nik Weaver Washington University

Title: A new approach to quantum metrics

Colloquium Thursday, 2/10/2005 Talk: 4:30, Tea: 4:00 Room: 199 Host: Prof. N. Mohan Kumar

Speaker: Prof. Hirotachi Abo Colorado State University

Title: Construction of non-general type smooth surfaces in projective fourspace

Abstract: Hartshorne conjectured that there exists a finite number of families of non-general type smooth surfaces in projective fourspace. In 1989, this conjecture was positively solved by Ellingsrud and Peskine. The exact bound for the degree is, however, still open. The question concerning the exact bound motivates us to attack the classification of nongeneral-type smooth surfaces of small degree. The most important step for solving this classification problem is to construct an example in each family of smooth nongeneral-type surfaces in projective fourspace. The main purpose of this talk is to construct a smooth rational surface of degree 12. The construction of this surface is reduced to finding a point of a 4-codimensional subvariety M of the grassmaniann G(10,4) of 4-quotient spaces in a 10-dimensional vector space. Over a finite field with q elements, the probability for a point in G(10,4) to lie in M is, therefore, about 1/q4. So we can expect to find such a point within a reasonable amount of time by picking points at random over a small field.

Wavelet Seminar Friday, 2/11/2005 Time: 3:30 Room: 199 Host: Prof. Guido Weiss

Speaker: Prof. Darrin Speegle Saint Louis University

Title: Feichtinger conjecture

Seminar Friday, 2/11/2005 Time: 4-5:30 Room: 111 Host: Prof. N. Mohan Kumar




Speaker: Professor Xiaofeng Sun Harvard University

Title: Analytic and Geometric Aspects of Moduli Space of Riemann Surfaces

Abstract: We introduce new metrics on the moduli and the Teichmuller spaces of Riemann surfaces, and study their curvatures and boundary behaviors by using the singular perturbation techniques from partial differential equations. These new metrics have Poincare growth near the boundary of the moduli space and have bounded geometry. Based on the detailed analysis of these new metrics, we obtain good understanding of all of the known classical complete Kahler metrics, in particular the Kahler-Einstein metric from which we prove that the logarithmic cotangent bundle of

the moduli space is stable in the sense of Mumford. By studying the Monge-Ampere equation together with the Kahler-Ricci flow on complete non-compact manifolds, we derive C^k estimates directly without using the C^0 estimate. Based on these analysis, we prove that the Kahler-Einstein metric has strongly bounded geometry. Another corollary is a proof of the equivalences of all of the known classical complete metrics to these new metrics, in particular Yau's conjectures on the equivalences of the Kahler-Einstein metric to the Teichmuller and the Bergman metric. We will also discuss the goodness of these metrics.

Graduate Seminar Tuesday, 2/15/2005 Time: 4:30-5:30, Pizza: 5:30-6 Room: 199 Host: Prof. Gary Jensen

Speaker: Joe Bohanon Washington University Graduate Student

Title: Planar Groups

Abstract: A group is called planar if its subgroup lattice can be drawn without edges crossing. In this talk, I will completely answer this question for finite groups. I will analyze abelian groups, $p$-groups, solvable groups, and nonsolvable groups in turn. There will be many pictures and sketches of proofs. This is a summary of a paper submitted by Les Reid and myself to the Journal of Algebraic Combinatorics.

Topology Seminar Wednesday, 2/16/2005 Time: 10:00am Room: 106 Host: Prof. Rachel Roberts

Speaker: Michael Hamm Washington University Graduate Student

Title: 3-manifold groups acting on the circle

Analysis Seminar Wednesday, 2/16/2005 Time: 4:00 Room: 199 Host: Prof. John McCarthy

Speaker: Leonid Kovalev Washington University Graduate Student

Title: Optimal transportation and the quasiconformal Jacobian problem

Abstract: The quasiconformal Jacobian problem, which originated in a 1990 paper of David and Semmes, asks for an analytic description of the Jacobian determinants of quasiconformal mappings. A part of this difficult problem is to characterize the singular sets of such Jacobians. We prove that every set of Hausdorff dimension less than 1 is a singular set for some quasiconformal mapping. The proof involves some ideas from the theory of optimal transportation, such as the Wasserstein metric. This is joint work with Diego Maldonado.

Colloquium Thursday, 2/17/2005 Tea 4:00 - Math Lounge Time: 4:30 - Room 199

Speaker: Prof. Emma Carberry Massachusetts Institute of

Title: Harmonic maps from Riemann surfaces to Lie groups and

Host: Prof. N. Mohan Kumar Technology symmetric spaces

Algebraic Geometry Seminar Friday, 2/18/2005 Time: 4:00 - Room: 111 Host: Prof. Gary Jensen

Speaker: Prof. N. Mohan Kumar Washington University

Title: Chern class formalism and the non vanishing of the hyperplane section class for projective schemes.

Graduate Seminar Tuesday, 2/22/2005 Time: 4:30-5:30 - Room 199 Pizza in the Lounge: 5:30-6:00 Host: Prof. Gary Jensen

Speaker: Prof. Ed Spitznagel Washington University

Title: Genes, gene-environment interaction, and the problem of quasicomplete separation in logistic regression.

Abstract: Logistic regression is a powerful tool in biostatistics, but its very nature precludes fitting cells with zero frequencies. This talk will present current solutions to the problem of observed (not structural) zeroes in logistic regression. I will begin the talk from first principles, with the definition of the logistic regression model.

Analysis Seminar Wednesday, 2/23/2005 Time: 4:00 - Room 199 Host: Prof. John McCarthy

Speaker: Gitta Kutyniok Visiting Research Assoc. Washington University

Title: A Decomposition Theorem for Frames and the weak Feichtinger Conjecture

Abstract: The so-called Feichtinger Conjecture, stating that every bounded frame can be written as a finite union of Riesz basic sequences, has recently gained attention beyond frame theory, since it is connected to the Kadison-Singer Conjecture from 1959. In this talk we will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. As an application of this result we will prove that the weak Feichtinger Conjecture is equivalent to the Feichtinger Conjecture. This is part of a project joint with P. G. Casazza (University of Missouri, Columbia) and D. Speegle (Saint Louis University).

William H. Roever Lecture Thursday, 2/24/2005 Tea 4:00 - Math Lounge Talk: 4:30 - Room 199 Host: Prof. Gary Jensen

Speaker: Prof. Alan Weinstein University of California Berkeley

Title: Morita equivalence in algebra and geometry

Abstract: The notion of Morita equivalence (of algebras or groupoids) leads to methods for treating certain ``pathological'' spaces in a reasonable way. In the course of describing this idea, I will explain how the quotient $R/(Z + \alpha Z)$, with $\alpha$ irrational, can be considered as a ``Lie group''. A good reference (not including the part on the "Lie group") would be my paper Bursztyn, H., and Weinstein, A., Poisson geometry and Morita equivalence, preprint math.SG/0402347, to appear in {\em Poisson Geometry, Deformation Quantization, and Group Representations}, LMS Lecture Note Series, Cambridge University Press, Cambridge.

Geometry Seminar Friday, 2/25/2005 Time: 10:00 - Room 199 Host: Prof. Gary Jensen

Speaker: Prof. Alan Weinstein University of California, Berkeley

Title: Poisson geometry near a Levi-nondegenerate hypersurface

Absract: Let M be a real hypersurface in a complex manifold X. The intersection of TM \cap J TM is a codimension 1 subbundle of TM; when it is a contact structure, M is said to be Levi nondegenerate. If \psi is a smooth function on X which vanishes without critical points everywhere on M, then the 2-form omega = i\partial \bar\partial (log psi) is a symplectic structure on the complement of M in a neighborhood of M in X; it blows up along M. We will show that the Poisson structure obtained by inverting omega extends smoothly across M and that, up to isomorphism near M, it is completely determined by the contact structure on M.

Vector Bundle Seminar Friday, 2/25/2005 Time: 4-5:30, Room: 111 Host: G.V. Ravindra

Speakers: Prof. A.P. Rao and G.V. Ravindra University of Missouri, Saint Louis/Washington University William Chauvenet Lecturer

Title: Chern classes of vector bundles on schemes and aplications.

MARCH


Speaker: Prof. John McCarthy Washington University

Title: Dirichlet series

Analysis Seminar Wedesday, 3/2/2005 Time: 4:00- Room 199 Host: Prof. John McCarthy

Speaker: Ilya Krishtal Washington University William Chauvenet Lecturer

Title: Exponential dichotomy for difference equations and invertibility of triangular matrices

Abstract: In my previous talk, I discussed connections between the spectrum of weighted-shift operators, exponential dichotomy of evolution families, and invertibility of two-diagonal matrices. This time, I will address similar issues concerning triangular matrices.

Colloquium Thursday, 3/3/2005 Tea: 4:00 - Math Lounge Talk: 4:30 - Room: 199 Host: Prof. Zhengjun Zhang

Speaker: Prof. Tiefeng Jiang University of Minnesota

Title: How Many Entries of A Typical Orthogonal Matrix Can Be Approximated By Independent Normals?

Abstract: I will present my solution to the well-known open problem by Diaconis. For more details: click HERE.

Wavelet Seminar Friday, 3/4/2005 Time: 3:30, Room: 199 Host: Prof. Guido Weiss

Speaker: Prof. Brody Johnson Saint Louis University

Title: Basic Applications of Wavelets

Algebraic Geometry Seminar Friday, 3/4/2005 Time: 4-5:30, Room: 111 Host: G.V. Ravindra

Speaker: G.V. Ravindra Washington University William Chauvenet Lecturer

Title: On the geometry of generalized quadrics

Colloquium Monday, 3/14/2005 Tea: 4:00 - Math Lounge Talk: 4:30 - Room 199 Host: Prof. Victor Wickerhauser

Speaker: Prof. Peter Fogh Odgaard Aalborg University, Denmark

Title: Wavelets and feature based control of Compact Disc players

Abstract: Many have experienced problems with the CD/DVD players when a CD or DVD with a scratch or fingerprint has been played. This presentation will introduce and describe a method which improve the CD/DVD players' ability to play disk which scratches and fingerprints. The problem is not to be found in the algorithm for error correction, but in two servo control loops, which are used to keep the Optical Pick-up Unit focused and radially on the information track of the disk. These control servos have problems handling surface faults on the disk. In my PhD thesis a method was proposed to improve the handling of these surface faults. The basic idea is to detect the surface faults, when the surface faults are detected, they are removed by an estimate of these surface faults based on previous encounter with the same faults. This method is formed by an improved localization of the surface faults based on a new couple of residuals, which is formed by a developed optical model and a fault model. Different

methods are developed to detect and localize the surface faults based on the residuals as well as an algorithm for classification of the surface faults. The useability of time/frequency bases, such as wavelets and wavelet packets, in these detection and classification methods are covered. The estimation of the surface faults are performed by Karhunen-Lohve approximations. In addition these approximations are used to simulate the surface faults in a simulation model. The proposed method have been tested by simulations and experiments, and the results of these are promising and interesting in terms of improvement of the optical disk drives playability of disks with surface faults.

Doctoral Dissertation Tuesday, 3/15/2005 Time: 10:00am, Room: 199

Speaker: Leonid Kovalev Washington University Graduate Student

Title: Orientation-preserving Sobolev mappings

Seiberg-Witten invariants Seminar Tuesday, 3/15/2005 Time: 2:40-4:00 Room: 210

Speaker: Jae-Hyouk Lee Washington University William Chauvenet Lecturer

Title: Spin and Spin^c connections


Speaker: Prof. Nan Lin Washington University

Title: Bayesian variable selection in multivariate linear regression

Analysis Seminar Wednesday, 3/16/2005 Time: 4:00 - Room 199 Host: John McCarthy

Speaker: Prof. Alexander Ulanovskii Purdue University

Title: Completeness of discrete translates

Abstract: Two classical theorems of N. Wiener assert that the linear span of the set of translates {f(t+c) ; c R} of a function f is dense in L1(R) (resp. L2(R)), iff f^(x) 0 for all x R (resp. if and only if f^(x) 0$ a.e.). Let us say that a real sequence C={cn ; n Z} admits a generator in Lp(R) if there is a function f Lp(R) such that the set of translates {f(t+cn) ; n Z} spans Lp(R). We ask which sequences C admit generators in Lp(R), p 1. In particular, we characterize sequences which admit generators in L1.

Colloquium Thursday, 3/17/2005 Tea: 400 - Math Lounge Talk: 4:30 - Room 199

Speaker: Prof. Hernando Ombao University of Illinois

Title: Analysis of Non-Stationary Time Series: An Overview of the

Host: Prof. Zhengjun Zhang Urbana-Champaign SLEX Methods

Abstract: Many biological and physical signals are non-stationary in nature. For example, brain waves recorded during an epileptic seizure have waveforms whose amplitude (variance) and oscillatory behavior (spectral distribution) change over time. This talk will address some of the interesting statistical problems in signal processing, namely, (i.) stochastic representations for non-stationary signals and model selection; (ii.) dimension reduction for massive multivariate nonstationary signals and (ii.) feature extraction and selection for classification and discrimination. I will present an overview of a coherent and unified body of statistical methods that are based on the SLEX (smooth localized complex exponentials) library. The SLEX are time-localized orthogonal Fourier waveforms with multi-resolution support. They are obtained by applying a projection operator on the complex exponentials. This projection operator was developed by Auscher, Weiss and Wickerhauser (1992) and it generalized previous constructions of localized sine and cosine bases by Malvar (1990) and Coifman and Meyer (1991). The SLEX library provides a systematic and efficient way of extracting transient spectral and cross-spectral features. In addition, the SLEX methods are able to handle massive data sets because they utilize computationally efficient algorithms. As a matter of practical importance, the SLEX methods give results that are easy to understand because they are time-dependent analogues of the classical Fourier methods for stationary signals. Finally, under the SLEX models, we develop theoretical results of consistency for spectral estimation and classification. The SLEX methods will be illustrated using biological and physical data sets, namely, brain waves, fMRI time series, a speech signal and seismic waves recorded during earthquake and explosion events. This talk will conclude with open and challenging problems in signal analysis and the potential of SLEX in addressing these.

Wavelet Seminar Friday, 3/18/2005 Time: 3:30, Room: 199 Host: Prof. Guido Weiss

Speaker: Alexi Savov Washington University Student

Title: Composite wavelets of finite type

Algebraic Geometry Seminar Friday, 3/18/2005 Time: 4:00-5:30, Room: 111 Host: Prof. N. Mohan Kumar

Speaker: Nikita Netsvetaev University of Missouri, Saint Louis/St. Petersburg State University

Title: Equations of subvarieties in projective space

Seiberg-Witten invariants Seminar Tuesday, 3/22/2005 Time: 2:40-4:00, Room: 210 Host: Prof. Quo-Shin Chi


Title: Gauge thoery and Seiberg-Witten eqaution

Graduate Seminar Tuesday, 3/22/2005 Time: 4:30-5:30 - Room 199 Pizza in the Lounge: 5:30-6:00 Room: 199 Host: Prof. Gary Jensen

Speaker: Ben Braun Washington University Graduate Student

Title: Graph Homomorphism Complexes

Abstract: Given two finite simple graphs G and H, a topological space HOM(G,H) can be built using families of graph homomorphisms from G to H. For specific G, different algebraic invariants of HOM(G,H) have been shown to give a lower bound for the chromatic number of H. We will discuss the construction of HOM(G,H) and survey some of these results, introducing necessary ideas from graph theory and algebraic topology along the way.


Speaker: David Opela Washington University Graduate Student

Title: Dilation Theorems

Abstract: I will discuss several types of dilation theorems for Hilbert spaces. Starting from a classical result of Arveson, to Popescu's theory, to some of my results. I will give proofs of some of the results.

Loeb Undergraduate Lecture Thursday, 3/24/2005 Tea: 4:00 - Math Lounge Cupples 1 - Room 200 Talk: 4:30, Crow Hall, Room 201

Speaker: Prof. Rick Laugesen University of Illinois Champaign-Urbana

Title: The Power and Beauty of Undergraduate Mathematics: Two Case Studies

Wavelet Meeting Friday, 3/25/2005 Time: 3:30, Room: 199 Host: Prof. Guido Weiss

Speaker: No speaker this week

Title: The application possibilities of composite dilation wavelets

Seiberg-Witten invariants Semniar Tuesday, 3/29/2005 Time: 2:40-4:00, Room: 210 Host: Prof. Quo-Shin Chi


Title: Seiberg-Witten invariants

Graduate Seminar Tuesday, 3/29/2005

Speaker: Prof. Victor

Title: Nonlinear filters for

Time: 4:30-5:30 - Room 199 Pizza in the Lounge: 5:30-6:00 Host: Prof. Gary Jensen

Wickerhauser Washington University

singularity detection and classification

Abstract: Using moments of the local Fourier transform of a function one can build nonlinear filters that distinguish singularity classes. The simplest cases are described in closed form, and an algorithm for the general case is presented.


Speaker: Gregory Knese Washington University Graduate Student

Title: A Schwarz Lemma on the Polydisk

Abstract: The infinitesimal portion of the classical Schwarz lemma on the disk gives an inequality on the first derivative of a given holomorphic function from the disk to the disk, and the functions for which equality holds at every point turn out to be the Mobius transformations. There is a simple generalization of this inequality for functions from the polydisk to the disk, for which we can completely describe the functions that satisfy equality at every point. We also provide some sufficient conditions for a function to satisfy equality at every point.

Colloquium Thursday, 3/31/2005 Tea: 4:00 - Math Lounge Talk: 4:30 - Room 199 Host: Prof. Al Baernstein

Speaker: Prof. David Drasin Purdue University

Title: Delta-subharminic functions and meromorphic functions

Abstract: If $f(z)$ is holomorphic, then $\log |f(z)|$ is subharmonic, and the same relation holds between meromorphic and delta-subharmonic functions. In many cases these two classes nearly coincide, and this gives a method to construct functions which has had many applications for the past half-century. We discuss some of the history and principles, and as an application present a solution to the problem of characterizing the set of asymptotic values of a moreomorphic functions of finite order (for entire funcitons, this is the famous Ahlfors theorem).

APRIL

Graduate Seminar Tuesday, 4/5/2005 Time 4:30-5:30 - Room 199 Pizza in the Lounge: 5:30-6:00 Host: Prof. Gary Jensen

Speaker: Jae-Hyouk Lee William Chauvenet Lecturer Washington University

Title: Vector Cross Product and Calibrated Geometry

Abstract: The Cross Product in $R^{3}$ can be generalized to the product of any number of tangent vectors, called the vector cross product. We will discuss that each vector cross product corresponds to certain type of Riemannian manifold and its geometric structures, for example, calibration. And based on the classification of vector cross products, we will also see a uniform approach to those geometric structures.

Analysis Seminar Wednesday, 4/6/2005 Time: 4:00, Room: 199 Host: Prof. John McCarthy


Title: Toral Varieties

Kirk Lecture Thursday, 4/7/2005 Tea: 4:00 - Math Lounge Talk: 4:30 - Room 199 Host: Prof. Renato Feres

Speaker: Prof. Lai-Sang Young Courant Institute, New York University

Title: Unraveling the Mystery of Strange Attractors

Abstract: I will discuss the emergence of chaotic behavior when external forcing is applied at periodic time intervals to very simple dynamical systems. This leads to the question "what exactly is a strange attractor?" which I will attempt to answer. Geometric and statistical properties of strange attractors will be discussed. I will provide the audience with a glimpse of some very recent developments in the mathematical theory of chaos, as well as their potential applications to the physical and biological sciences and engineering.


Speaker: Prof. Guido Weiss Washington University

Title: On Shift Invanriant Spaces

Algebraic Geometry Seminar Friday, 4/8/2005 Time: 4-5:30 Room: 111 Host: Prof. N. Mohan Kumar

Speaker: Zemin Zeng Washington University Graduate Student

Title: The Euler Class group

Minor Oral Tuesday, 4/12/2005 Time: 1:00 Room: 199 Host: Prof. N. Mohan Kumar

Speaker: Bennet Standeven Washington University Graduate Student

Title: Classifying Norms on the Rationals

Graduate Seminar Tuesday, 4/12/2005

Speaker: Ilya Krishtal

Title: Conjectures of Kadison-Singer

Time: 4:30-5:30 - Room 199 Pizza in the Lounge: 5:30-6:00 -Math Lounge Host: Prof. Gary Jensen

William Chauvenet Lecturer Washington University

and Feightinger and some surprisingly(?) related things in between

Abstract: I will describe several seemingly unrelated conjectures in different areas of mathematics ranging from C*-algebras to the frame theory. We shall discuss some amazing connections between them and some partial results.

Analysis Seminar Wednesday, 4/13/2005 Time: 4:00-5:00, Room 199 Host: Prof. John McCarthy

Speaker: Prof. Alexander Fryntov Purdue University

Title: Some estimates for the length of polynomial lemniscates

Abstract: Let $p(z)$ be a monic polynomial of a fixed degree $n\ge 1$. Consider a curve $$ L_p := \{z:\, |p(z)|=1\} $$ which is called a lemniscate of the polynomial $p$. Denote its length by $|L_p|$. A famous Erd\"os conjecture asserts that \begin{equation}\label{eq:1} |L_p|\le |L_{q}|\,. \end{equation} where $q(z)=z^n+1$. The goal of the talk is to give a new approach to upper estimates of lemniscate length based on the Stocks formula with demonstration of some intermediate results\,.

Colloquium Thursday, 4/14/2005 Time: 4:00-Rm. 199 Host: Prof. Rachel Roberts

Speaker: Prof. Gordana Matic University Georgia

Title: Contact structures on 3-manifolds and surface homeomorphisms

Abstract: Thurston and Winkelnkemper have used existence of open book decompositions to show that any 3-manifold carries a contact structure. Giroux proved a converse, and more. He showed that contact structures on 3-manifolds correspond to certain equivalence classes of open book decompositions and characterized Stein fillable structures as those admitting open books with gluing homeomorphisms that are compositions of positive Dehn twists. We introduce a class of homeomorphisms that corresponds to tight contact structures and discuss some examples.



Title: The dimension function and all that

Wavelet Seminar Friday, 4/15/2005

Speaker: Prof. Guido Weiss

Title: The dimension function

Time: 3:30 Room: 199 Host: Prof. Guido Weiss

Washington University

and all that





Speaker: G.V. Ravindra William Chauvenet Lecturer Washington University

Title: Vector bundles on projective spaces

Abstract: We shall give a necessary and sufficient condition for a vector bundle to be a sum of line bundles. This is a theorem due to Horrocks.


Speaker: Prof. Richard Rochberg Washington University

Title: Carleson Measures for0 some Function Spaces

Colloquium Thursday, 4/21/2005 Time: 4:30pm Room: 199 Host: Prof. Gary Jensen

Speaker: Chumning Zhang Assistant Professor University of Wisconsin

Title: Model Selection Criteria for Local-Likelihood and Semiparametric Regression

Abstract: Local-likelihood regression is a versatile nonparametric technique for exponential family responses. The issues of optimal smoothing based on model selection criterions are investigated. We propose a model selection criterion function (MSCF), based on a broad $Q$-class of Bregman divergence for prediction error measures which embeds nearly all of the commonly used loss functions in regression, classification procedures and machine learning literature. We find that this MSCF differs from the traditional mean-integrated-squared-error (MISE) criterion, with an exception of the Gaussian data using the canonical link. We then study the data-driven bandwidth selector that minimizes the prediction error estimates or equivalently the covariance penalty function. A cross-validated estimation of the $Q$-class prediction errors is proposed. The approximate formulas for leave-one-out local-likelihood estimator are derived to facilitate the computation of the local-likelihood estimator. It is shown that the covariance penalty and cross-validation methods converge to the same MSCF. Finally, we propose a lower-bound scheme for computing the local logistic

regression and demonstrate that it is as simple and stable as the local least-squares regression. The algorithm monotonically increases the target local-likelihood and converges. The idea and methods are extended to the generalized varying-coefficient models and semiparametric models. Application to information-theoretical learning will also be illustrated.




Graduate Seminar Tuesday, 4/26/2005 Time: 4:30-5:30 - Room 199 Pizza in the Lounge: 5:30-6 Host: Prof. Gary Jensen

Speaker: Prof. Rachel Roberts Washington University

Title: Handle decompositions of manifolds

Abstract: We begin with a discussion of Euler characteristic, move to a discussion of vector fields, and then as time permits, discuss handle descriptions of n-manifolds.


Speaker: Paul Koester Washington University Graduate Student

Title: Multilinear Averages and the Growers Uniformity Norms

Abstract: We discuss certain multilinear averages that appear in Gowers' proof of Szemer\"{e}di's theorem on arithmetic progressions. For short progressions one can use simple Fourier analytic estimates, but these methods no longer work for longer progressions. The problem is that the k-linear form used to count k-term arithmetic progressions enjoys a certain invariance under polynomial phase shifts for polynomials of degree k-2, and traditional "linear" Fourier analysis can only handle linear phase shifts. Gowers introduced the uniformity norms to get control over these higher degree phase shifts.


Speaker: Sooraj Kuttykrishnan Washington University Graduate Student

Title: Linear triangularization and jacobian conjecture in dimension 3, Part II

MAY

Minor Oral Exam Wednesday, 5/4/2005 Time: 4:00 Room: 199 Host: Prof. John McCarthy

Speaker: Prasada Vegulla Washington University Graduate Student

Title: Capacity & Hausdorff measure in Rn


Speaker: Ilya Krishtal Washington University William Chauvenet Lecturer

Title: Perturbation of frame sequences in shift-invariant spaces

Algebraic Geometry Seminar Monday, 5/9/2005 Time: 1:00 Room: 199 Host: Prof. N. Mohan Kumar

Speaker: Francesco Malaspina University of Missouri, Saint Louis

Title: Monads on Quadrics

Colloquium Monday, 5/9/2005 Tea: 4-4:30, Talk: 4:30-5:30 Room: 199Host: Prof. N. Mohan Kumar

Speaker: Prof. S.M. Bhatwadekar Tata Institute of Fundamental Research, Mumbai, India

Title: Projective modules and real affine algebras

Abstract: Let $A$ be a smooth affine algebra of dimension $n$ over a field $k$ and $P$ be a finitely generated projective $A$-module of rank $n$. In the case $k={\bf C}$, the field of complex numbers, a result of Murthy says that $P$ splits off a free summand of rank one if and only if the top Chern class $C_{n}(P)$ of $P$ in $CH_{0}(A)$ is zero. However, in the case $k={\bf R}$, the field of real numbers, this result in not true in general. For example, if $A$ is the coordinate ring of an even dimensional real sphere and $P$ is the tangent bundle, then it is well known that $P$ does not split off a free summand of rank one even though $C_{n}(P)=0$. Incidentally, all the known examples of projective modules exhibiting such a behaviour are over even dimensional real affine algebras. Therefore, it is natural to ask :\\ {\it Let $A$ be a smooth affine algebra of odd dimension over the field of real numbers and let $P$ be a projective $A$-module of rank $n$. Does $P$ split off a free summand of rank one if $C_{n}(P)=0$?} In my talk I will address this question and show that the question has an affirmative answer in many cases.

Analysis Conference Thursday, 5/12/2005 Time: 8:15-5:15, Crow Hall, Rm. 201

Speakers: Alexander Eremenko, Purdue University Alexander Solynin,

Title: TBA

Texas Tech University Allen Weitsman, Purdue University John Garnett, UCLA Jang-Mei Wu, University of Illinois

Analysis Conference Friday, 5/13/2005 Time: 8:15-5:15, Crow Hall, Rm. 201

Speakers: John Lewis, University of Kentucky Jill Pipher, Brown University Michael Loss, Georgia Tech University Rodrigo Bañuelos, Purdue University Burgess Davis, Purdue University

Title: TBA

Analysis Conference Saturday, 5/14/2005 Time: 8:15-4:55, Crow Hall, Rm. 201

Speakers: Roger Barnard, Texas Tech University Kari Astala, University of Helsinki Daniel Shea, University of Wisconsin Richard Rochberg, Washington University Daniel Girela,University of Malaga Carlo Morpurgo, University of Missouri Almut Burchard, University of Virginia Juan Manfredi,

Title: TBA

Pittsburgh University

SEPTEMBER

Topology Seminar Wednesday, 9/14/2005 Time: 1-2:30pm Location: Cupples I, Room 106 Hostess: Prof. Rachel Roberts

Speaker: Aaron Wiechmann Graduate Student, Washington University

Title: Thin Position, Part II

Algebraic Geometry Seminar Wednesday, 9/14/2005 Time: 4-5:30pm Location: Cupples I, Room 199 Host: Prof. N. Mohan Kumar

Speaker: Karen Chandler UMSL

Title: Multiple Base points of a Linear Series

Undergraduate Math Club Monday, 9/19/2005 Time: 5:00-6:30pm Location: Cupples I, Room 222 Host: Prof. Guido Weiss

Speaker: Prof. Robert H. McDowell Washington University

Title: Approaches to Infinite

Graduate Seminar Tuesday, 9/20/2005 Time: 5:30-6:30pm Location: Cupples I, Room 199 Host: Prof. Quo-Shin Chi

Speaker: Prof. Renato Feres Washington University

Title: Harmonic Functions on Orbits of Discrete Group Actions


Speaker: Prof. Karen Chandler UMSL


Wavelet Seminar Friday, 9/23/2005 Time: 3:30pm Location: Cupples I, Room 199 Host: Prof. Guido Weiss

Speaker: Prof. Wenjie He University of Missouri in St. Louis

Title: Nonstationary wavelet tight frames

Abstract: We extend the theory of stationary wavelet tight frames with the affine structure to that of nonstationary wavelet tight frames that only rely on the structure of the nested subspaces of L_2. In order to achieve arbitrary order of vanishing moments

for the tight frames, we introduce the notion of the approximate duals and the Vanishing Moment Recovery (VMR) matrices. We give a characterization for the locally supported nonstationary wavelet tight frames. We apply this theory to the spline functions on arbitrary nested knot sequences and develop constructive schemes. The results presented in this talk are from three ACHA papers of Chui, He, and Stoeckler.

Analysis Seminar Monday, 9/26/2005 Time: 4:00-5:00pm Location: Cupples I, Room 199


Title: Univalent functions into $C^2$

Toric Geometry Seminar Monday, 9/26/2005 Time: 4:00-5:30pm Location: Cupples I, Room 216 Host: Prof. Jaehyouk Lee

Speaker: Prof. G.V. Ravindra William Chauvenet Lecturer, Washington University

Title: Toric Varieties 1


Speaker: Prof. Gary R. Jensen Washington University

Title: How Did Archimedes Estimate Pi?

Abstract: Among the many accomplishments of Archimedes of Syracuse (287 - 212 BC) is his estimate 3 10/71 < pi < 3 1/7. How did he arrive at this? Fortunately, he left a written record of how he did it, and I'll go through this. But he doesn't explain anywhere how he estimates the square roots that are needed in his method. For example, without further comment he writes 265/153 < sqrt(3) < 1351/780. How do you think he got this? Mixed into the talk will be discussion of the definition of pi (the wrong one got one person fired) and a mnemonic for remembering the first 24 digits in the decimal expansion of pi.


Speaker: Prof. Stanley Sawyer Washington University

Title: How Can One Tell In What Direction Evolution is Going?

Abstract: In the long run, most important changes in biological organisms are due to the replacements of genes by new genes that do a better job for the organism. However, in large, established populations, many biologists believe that most evolutionary change is, instead, due to the replacement of genes by slightly deleterious variants. The reason for this is that most mutations are harmful rather than helpful, and that mildly harmful mutations can replace a better, established gene by the chance effects of who

mates with whom and who happens to survive. This would take a long time for a large population, but most large populations have been around for a very long time. We can study this question from the distribution of DNA in populations in the present. The distribution of a new gene is different if it is advantageous, deleterious, or selectively the same as the old gene. We can also consider differences between two related species. Crude measurements suggest that most recent historical changes in fruit flies were advantageous, but that most changes in a common weed were deleterious. Investigating this process more rigorously leads to difficult problems in probability theory and statistics.

Special Talk Thursday, 9/29/2005 Time: 4:00-5:00pm Location: Cupples I, Room 199


Title: Mathematical Conceptualism

Abstract: Is circular reasoning necessary in mathematics? Many mainstream mathematicians might be surprised to learn that logicians generally concede that the standard axiomatizations of set theory involve deep, fundamental circularities. Mathematical conceptualism is an alternative foundational philosophy, originating in views of Poincare and Russell, which strictly forbids all circularity. This sort of approach was originally thought to be far too weak to support ordinary core mathematics, and later was felt to be subject to severe limitations of a more abstract nature, but we now know that these limitations are not valid and in fact essentially all core mathematics is conceptualistically legitimate if interpreted properly. At the same time, conceptualism exorcises vast regions of set-theoretic pathology from the mathematical universe, so that it is in fact in better accord with actual mathematical practice than the Cantorian picture. I believe a strong case can be made for abandoning Cantorian set theory as a foundation for mathematics, and adopting conceptualism in its place.

Wavelet Seminar Friday, 9/30/2005 Time: 3:30pm Location: Cupples I, Room 199 Host: Prof. Guido Weiss

Speaker: Prof. Qingtian Jiang University of Missouri in St. Louis

Title: Construction of Refinable Functions/Vectors

Abstract: In this talk we will discuss the construction of refinable functions and refinable function vectors for surface subdivision applications. First, we will show briefly how the refinable functions/vectors are used to derive the so-called local averaging rules in subdivision. Then we will consider certain dilation matrices which are used for square-root 2, square-root 3, square-root 5, and square-root 7 subdivisions. Finally, we will introduce the procedures to construct refinable functions/vectors and present some examples.

OCTOBER

Analysis Seminar Monday, 10/3/2005 Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. John McCarthy


Title: Analysis in J_2

Abstract: Abstract: I will explain how core mathematics, particularly abstract analysis, can be developed within a concrete countable set J_2 (the second set in Jensen's constructible hierarchy). The implication, well-known to proof theorists but probably not to most mainstream mathematicians, is that ordinary mathematical practice does not require an enigmatic metaphysical universe of sets.





Speaker: Prof. Prof. Edward N. Wilson Washington University

Title: Quaternions and Their Applications to Geometry


Speaker: Prof. N. Mohan Kumar Washington University

Title: Complete Intersections and Hartshorne's Conjecture


Speaker: Prof. Karen Chandler UMSL


Wavelet Seminar Friday, 10/7/2005 Time: 2:30pm Location: SLU McDonnell Douglas Hall, Room 1016 Hosts: Prof. Guido Weiss & Prof. Brody Johnson (SLU)

Speaker: Prof. Kasso Okoudjou Cornell University

Title: On some Fourier multipliers for modulation spaces

Abstract: In this talk, I will use some time-frequency analysis techniques to study the continuity properties of a class of Fourier multipliers on the modulation spaces. In particular, I will consider Fourier multipliers related to certain evolution equations, and which are known to be unbounded on Lebesgue spaces.



Title: Interpolation of values by functions in the Dirichlet space





Speaker: Brian Maurizi Graduate Student, Washington University

Title: The Logistic Equation

Abstract: Is there anything you don't know about the innocuous quadratic equation f(x) = ax(1-x) ? Probably more than you would believe. For the right values of a, this function maps [0,1] -> [0,1] , and the dynamical system it creates has some bizarre properties. We will look at some basic ideas of iteration, attractors, and that perennial buzzword, chaos.



Title: Zeros of analytic functions

Abstract: Any n points in the complex plane can be the zero set of a polynomial of degree n. The corresponding questions and answers for analytic functions are more complicated.

Minor Oral Monday, 10/17/2005 Time: 3:00-4:00pm Location: Cupples I, Room 199

Speaker: Amei Graduate Student, Washington University

Title: Diffusion approximation to discrete-time Markov processes

Host: Prof. Stanley Sawyer

Abstract: Consider a monoecious population of N individuals with two alleles A and a at a particular locus under selection and mutation. If p_n is the frequency of the allele A at the beginning of the nth generation, the distribution of p_n+1 given p_n is binomial, hence {p_n} forms a discrete-time Markov process on a finite state space. A diffusion approximation to discrete-time Markov processes can be used to calculate the probability that the population becomes all A-genes and the mean time of the population to fix at either one of the two genes by solving differential equations.

Minor Oral Monday, 10/17/2005 Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. Nik Weaver

Speaker: Bo Zhao Graduate Student, Washington University

Title: Introduction to Subfactors

Abstract: What's the possible values of the index [M:N] where here N,M is the inclusion of II1 factors. V. Jones showed in his 1983 paper that the set of values contains a discrete and a continuous part. In this talk, I will talk about what is the II1 factor, some examples, and the basic construction that leads to get the above result.






Title: Tarski's "high school algebra" problem

Abstract: In high school we learn that the natural numbers obey a list of 11 axioms (commutativity, associativity, and distributivity of + and x; 1 is a multiplicative unit; and the exponential axioms 1^x = 1, x^1 = x, x^(y+z) = x^y x^z, (xy)^z = x^zy^z, and (x^y)^z = x^(yz)). Is this list complete? That is, are there any other true identities involving +, x, and ^ which are not consequences of the ones listed above? This is Tarski's ``high school algebra'' problem. The answer may surprise you!

Graduate Seminar Tuesday, 10/18/2005 Time: 5:30-6:30pm

Speaker: Prof. Gary R. Jensen Washington

Title: Problems in Lie Sphere Geometry

Location: Cupples I, Room 199 Host: Prof. Quo-Shin Chi

University

Abstract: What properties of a surface in 3-space remain unchanged by reflection in a sphere, or by displacement of each point of the surface a fixed distance along a continuous normal vector field? These reflections, together with rigid motions, are the transformations of conformal geometry. All of these with the parallel transformations constitute Lie sphere geometry. How to study the properties unchanged by these transformations will be explained in the elementary context of surfaces in 3-space. Several elementary open problems will be proposed.

Colloquium Thursday, 10/20/2005 Time: Tea: 4:00pm Colloquium: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Albert Baernstein II

Speaker: Prof. Marco Peloso University of Torino, Italy University of Missouri-Columbia

Title: Spectral analysis of the Hodge Laplacian on the Heisenberg group

Abstract: On a smooth manifold M, the Hodge Laplacian is the second order, self-adjoint differential operator -(dd*+d*d), acting on k-forms. In the theory of this operator, the interplay between analysis, geomtry and topology are striking. In this talk I will present some results concerning the analysis of this operator on the Heisenberg group and some quotients of it. In particular, we obtain a sharp multiplier theorem of Mihilin-Hormander type, determine the eigenvalues on some compact quotients of the Heisenberg group, and calculate the Novikov-Shubin invariants on a non-compact quotient. (These results are in collaboration with D. Muller and F. Ricci.)

Topology Seminar Friday, 10/21/2005 Time: 2:00-3:00pm Location: Cupples I, Room 199 Hostess: Prof. Rachel D. Roberts

Speaker: Prof. Steve Hurder University of Illinois at Chicago

Title: Construction of generalized Hirsch Foliations

Analysis Seminar Monday, 10/24/2005 Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. Albert Baernstein II

Speaker: Prof. Ignacio Uriarte-Tuero University of Missouri-Columbia

Title: On Marcinkiewicz integrals and harmonic measure

Abstract: Jones and Makarov gave sharp density estimates for harmonic measure using a modified version of Marcinkiewicz integrals called $\tilde I_{0}$. It was also used by Jones and Smirnov to substantially advance in the Sobolev and quasiconformal removability problems. We generalize and slightly change $\tilde I_{0}$ to make it account for different densities of sets over which to integrate, in particular giving a different proof than Jones' and Makarov's of its key properties. This should have

applications to the aforementioned Sobolev and quasiconformal removability problems. The techniques used are essentially stopping time and other harmonic analysis arguments.





Speaker: Prof. John Shareshian Washington University

Title: Representation theory of symmetric groups.

Abstract: I will begin with a short discussion of the representation theory of finite groups, a powerful tool that was discovered near the end of the 19th century. Almost as old is the close study of a particular case, the representation theory of symmetric groups. This special case involves various combinatorial techniques which produce much better results than those known in the general case. I will describe the representation theory of symmetric groups and present one, two or three open problems, as many as time permits.


Speaker: Karen Chandler UMSL


Colloquium Thursday, 10/27/2005 Time: Tea: 4:00pm Colloquium: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Prof. Alexander Borichev University of Bordeaux, France

Title: Weighted polynomial approximation on the real line

Abstract: Suppose we have a positive function $w$ on the real line. What functions can be approximated by the polynomials on the real line with weight $w$? We discuss the history of the weighted polynomial approximation problem and some recent developments.

Topology Seminar Speaker: Prof. Title: Construction

Friday, 10/28/2005 Time: 2:00-3:00pm Location: Cupples I, Room 199 Hostess: Prof. Rachel D. Roberts

Steve Hurder University of Illinois at Chicago

of generalized Hirsch Foliations

Wavelet Seminar Friday, 10/28/2005 Time: 3:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Guido Weiss

Speaker: Prof. Darrin Speegle St. Louis University

Title: Parseval Frame Wavelets

Abstract: The talk will serve as an introduction to the talk Prof. Hrvoje Sikic will give on the following Friday. It is devoted to a collaboration Prof. Sikic is involved in with Prof. Speegle and Prof. Weiss.

Analysis Seminar Friday, 10/28/2005 Time: 4:00-5:00pm Location: Cupples I, Room 215 Host: Prof. John McCarthy

Speaker: Prof. Alexander Borichev University of Bordeaux, France

Title: Uniqueness theorems for the Korenblum space

Abstract: We find the maximal possible decay of the Korenblum space functions along uniqueness sets. The extends earlier work of Lyubarskii-Seip concerning the space $H^\infty$.


Speaker: Paul Koester Graduate Student, Washington University

Title: Graph Regularity

Abstract: The Szemeredi regularity lemma allows one to approximate large and complicated graphs by much simpler graphs. This is a very powerful tool in extremal combinatorics. We will discuss this lemma along with some applications to graph theory, number theory, and discrete geometry.




Undergraduate Math Club Speaker: Prof. John Title: Permutation

Monday, 10/31/2005 Time: 5:00-6:30pm Location: Cupples I, Room 222 Host: Prof. Guido Weiss

Shareshian Washington University

Statistics

NOVEMBER


Speaker: Amei Graduate Student, Washington University

Title: Diffusion approximation to discrete-time Markov processes

Abstract: Consider a monoecious population of N individuals with two alleles A and a at a particular locus under selection and mutation. If p_n is the frequency of the allele A at the beginning of the nth generation, the distribution of p_n+1 given p_n is binomial, hence {p_n} forms a discrete-time Markov process on a finite state space. A diffusion approximation to discrete-time Markov processes can be used to calculate the probability that the population becomes all A-genes and the mean time of the population to fix at either one of the two genes by solving differential equations.

Seminar Wednesday, 11/2/2005 Time: 4:00- Location: Rebstock, Room 322 (Reception following in Room 309) Host: Prof. Ralf Quatrano, Biology Department

Speaker: Prof. Alex Mogilner University of California, Davis

Title: Computational modeling of mesoscopic molecular machines: from mitotic spindle to lamellipodium, from biophysics to system biology


Speaker: Prof. Prabhakar Rao UMSL

Title: ACM bundles on hypersurfaces


Speaker: Prof. Hrvoje Sikic University of Zagreb, Croatia

Title: This is a continuation of Professor Speegle's (10-28-05) talk.


Speaker: Prof. Ilya Krishtal William Chauvenet Lecturer, Washington University

Title: Coercivity of operator matrices, sampling, and localization of frames

Abstract: We consider operator matrices which define bounded linear operators on l^p for all p. We prove that if such an operator is bounded below (coercive) for some p, then, under some conditions, it is also coercive for all other p. We discuss the implications of this result for sampling/reconstruction theory and Banach frame theory.


Speaker: Prof. Jaehyouk Lee William Chauvenet Lecturer, Washington University

Title: Toric Manifolds and Moment map (Part I)



Title: Fourier Series

Abstract: As many of the important facts about Fourier Series as can be presented in a short 40 minute lecture will be talked about. If this lecture is icredibly well received and the crowd of listeners want to know more, another such lecture will be given in the future.


Speaker: Prof. David L. Wright Washington University

Title: Polynomial Automorphisms: the Great Unknown




Colloquium Thursday, 11/10/2005

Speaker: Prof. Harold R. Parks

Title: Generalizing Faulhaber's

Time: Tea: 4:00pm Colloquium: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. Steven G. Krantz

Oregon State University

Formula to Non-Integral Powers

Abstract: The familiar formulas for the sum of the first N positive integers and for the sum of the squares of the first N positive integers are special cases of a formula for the sum of any positive-integral power of the first N positive integers. This more general formula is attributed to Johann Faulhaber (1580-1635) and can be neatly expressed using the Bernoulli numbers. Faulhaber's formula has a surprisingly nice generalization to non-integral powers that I will describe. The almost entirely elementary proof will be sketched.


Speaker: Prasad Vegulla Graduate Student, Washington University

Title: Parametrizing distinguished varieties of rank (m,n)

Abstract: Distinguished Varieties are varieties that exit the bidisk through the distinguished boundary i.e, the torus. Their importance arises in connection with the study of extremal Pick problems on the bidisk, Ando's inequality and certain other problems. John McCarthy & Jim Agler have obtained some results on parametrizing these varieties for some specific cases. We generalize their results further.


Speaker: Prof. Jaehyouk Lee William Chauvenet Lecturer, Washington University

Title: Toric Manifolds and Moment map (Part II)



Title: Calculus Models for Real Data

Abstract: Textbook examples using calculus to describe real situations are often artificial and/or exotic. I'll describe some situations where the same ideas can be used to describe commonplace, and hopefully interesting, situations.

Major Oral Tuesday, 11/15/2005

Speaker: Ben Braun

Title: Coefficients and Roots of

Time: 4:15-5:15pm Location: Cupples I, Room 199 Host: Prof. John Shareshian

Graduate Student, Washington University

Ehrhart Polynomials

Abstract: Given a d-dimensional polytope P in R^d whose vertices are all in Z^d, a theorem of Ehrhart states that the number of lattice points in the n-th dilate of P is given by a degree d polynomial in n. We will discuss the basics of Ehrhart theory and what is currently known about coefficients and roots of Ehrhart polynomials.


Speaker: Prof. Edward N. Wilson Washington University

Title: TBA

Algebraic Geometry Seminar Wednesday, 11/16/2005 Time: 4:00-5:30pm Location: Cupples I, Room 199 Host: Prof. N. Mohan Kumar



Colloquium Thursday, 11/17/2005 Time: Tea: 4:00pm Colloquium: 4:30-5:30pm Location: Cupples I, Room 199 Host: G.V. Ravindra

Speaker: Prof. Andreas Rosenschon SUNY-Buffalo

Title: Rigidity

Abstract: Let F be a cohomology theory with torsion values which is defined for smooth varieties over fields. Given an extension K/k of fields, we ask when one has rigidity in the sense that the map F(X)\rightarrow F(X_K) is an isomorphism. For example, this is known to hold in case K/k is an extension of algebraically closed fields, and F is etale cohomology or algebraic K-theory (with finite coefficients). We prove the analogous result for other types of field extensions (not necessarily algebraically closed) in case F belongs to a certain class of theories including, for example, algebraic $K$-theory, motivic cohomology, and etale cohomology (with finite coefficients). We outline how to prove a similar result for algebraic cobordism. This talk will be aimed at nonexperts, and reports on joint work with {\O}stv{\ae}r.



Title: Haar measures


Speaker: Greg Knese Graduate Student, Washington University

Title: Caratheodory Distance on the Neile (Semi-Cubical) Parabola in the Bidisk

Abstract: The Caratheodory distance is an important biholomorphic invariant for a complex space. Unfortunately, like many abstract objects, it is difficult to compute explicitly. We present the first explicit computation of this distance for a variety with a singularity; namely, for the so-called Neile parabola (z^2=w^3 for (z,w) in the bidisk). In addition, we relate this computation to an interpolation problem (on the disk) of a type not directly accessible using the known theorems of Pick and Caratheodory (and their generalizations). Finally, we shall mention a simple extension result for bounded holomorphic functions from the Neile parabola to the bidisk.

Combinatorial Commutative Algebra Seminar Tuesday, 11/22/2005 Time: 4:15-5:30pm Location: Cupples I, Room 199 Host: Prof. John Shareshian

Speaker: Sooraj Kuttykrishnan Graduate Student, Washington University

Title: Groebner basis- Part II



Title: A general description of Wavelets for those not in this field

Abstract: Many, who are not working on 'wavelets' have voiced an interest in finding out what the subject is all about. I have been asked to give two colloquium talks on this subject to general audiences in other universities. I told them that I am happy to do so and I welcome all (students, engineers, algebraists, topologists, Cub or Cardinal fans and even White Sox fans) to come, criticize and ask questions. The talk to the Graduate seminar will be a 'practice talk' for these two colloquia.

Major Oral Monday, 11/28/2005 Time: 4:00-5:00pm Location: Cupples I, Room 199 Host: Prof. Albert Baernstein II

Speaker: James Gill Graduate Student, Washington University

Title: Area Distortion in Quasiconformal Mappings

Abstract: Quasiconfromal mapppings in the plane can be roughly thought of as homeomorphisms which take infinitesimal circles to infinitesimal ellipses, as opposed to conformal mappings which take them to infinitesimal circles. In 1992 Astala found a proof to a long conjectured inequality on the area distortion of a normalized class of

these mappings. Shortly thereafter Eremenko considerably shortened Astala's proof and Hamilton sharpened the theorem. This lead to a joint 1995 paper which will be the topic of this lecture.


Speaker: Prof. Albert Baernstein II Washington University

Title: You might go home again: Recurrence and transience of symmetric random walks in the first three dimensions

Abstract: Suppose you start at the origin of the real line, toss a fair coin, then move one step to the right or left according as the coin falls heads or tails. Repeat the process, starting from your new position, then repeat again and again, ad infinitum. This process has evident analogues in all dimensions. What is the probability that you will ever return to your starting point? In particular, will you return with probability 1, or is there a positive probability you will never return? We'll see that the answer depends upon the dimension of the world you live in.


Speaker: Prof. Jae-Hyouk Lee William Chauvenet Lecturer, Washington University

Title: How to define Symplectic Grassmannian Spaces

Abstract: As Complex Grassmannian spaces are Grassmannian spaces with complex geometry, we can consider Grassmannian spaces with symplectic geometry. We will discuss what is a proper way to define symplectic Grassmannian spaces and their geometries.



Title: ACM bundles on hypersurfaces (Continued)

DECEMBER

Undergraduate Math Club Monday, 12/5/2005 Time: 5:00-6:30pm Location: Cupples I, Room 222

Speaker: Prof. Renato Feres Washington University

Title: The mathematics of billiards

Host: Prof. Guido Weiss

Abstract: The motion of a billiard ball on tables of irregular shapes is an example of a purely deterministic mechanical system that can be investigated by probabilistic means, if the geometry of the billiard table is sufficiently dispersing. In this talk, I will describe a few results relating statistical properties of billiard orbits and the shape of the billiard table.


Speaker: Prof. Albert Baernstein II Washington University

Title: Bloch functions, BMOA functions and hyperbolic metrics

Abstract: A complete Riemannian metric of constant Gaussian curvature on a domain D in the complex plane is called a hyperbolic metric on D. Analytic functions on D which are Lipschitz with respect to the induced hyperbolic distance are called Bloch functions. The Bloch functions contain as interesting subclass the set of analytic functions of bounded mean oscillation on D. In this talk we shall discuss various properties of these objects, and shall examine the famous open problems of finding the exact values of the covering constants of Bloch and Landau.


Speaker: Prof. David L. Wright Washington University

Title: A Combinatoric Approach to the Jacobian Conjecture

Colloquium Thursday, 12/8/2005 Time: Tea: 4:00pm Colloquium: 4:30-5:30pm Location: Cupples I, Room 199 Host: Prof. John McCarthy

Speaker: Prof. Robert Pless Washington University

Title: Parameterizing Natural Video through Manifold Learning

Abstract: Video data sets that depict various complicated motions --- such as flying birds, walking people, and cine-MRI of beating hearts --- may have a small number of intrinsic degrees of freedom. This work attempts to find and characterize these degrees of freedom by extending Isomap, a recently popularized, data driven manifold learning learning algorithm. This general tool for dimensionality reduction defines a neighborhood graph between points in the high-dimensional space, estimates geodesics as shortest paths through this neighborhood graph, then finds a low-dimensional embedding that preserves these geodesic distances (using Multi-Dimensional Scaling). In this talk I will discuss modifications of this method that make it effective with natural images and video. I will conclude by formalizing several open questions in

manifold learning --- especially in parameterizing data sampled from manifolds that are homeomorphic to spheres, cylinders or tori, that currently limit their application to real problems.


Speaker: Prof. Demetrio Labate North Carolina State University

Title: Optimally Sparse Multidimensional Representation using Shearlets

Abstract: We show that the shearlets, recently introduced by the authors and their collaborators, provide an essentially optimal representation for 2--dimensional functions that are $C2$ apart from discontinuities along $C2$ curves. Unlike the curvelets, that have similar approximation properties, the shearlets form an affine-like system. Indeed, they are generated by applying dilations, shear transformations and translations to a well-localized window function, and are associated to a generalized multiresolution analysis. This mathematical structure is especially useful for the fast algorithmic implementation of shearlets as well as for their generalizations to higher dimensions. This represents a collaboration with K. Guo.


Speaker: David Opela Graduate Student, Washington University

Title: Interpolating and Sampling Sequences in Holomorphic Spaces

Abstract: A sequence z_n of points is an interpolating sequence for H, if for any reasonable (in terms of size) prescribed values w_n there exist a function in H such that f(z_n)=w_n. It is a sampling sequence, if one can recover f from its values on this sequence so that the 'size' of the values is comparable to the norm of f. I will talk about what is know about these sequences for classical holomorphic spaces, their multiplier algebras and connections with the Pick property.


Speaker: Aaron Wiechmann Graduate Student, Washington University

Title: Surgery on the 3-Sphere

2005 - Talksequation together with the Kahler-Ricci flow on complete non-compact manifolds, we...

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